Block-Entropy Analysis of Climate Data

Abstract

We explore the use of block entropy as a dynamics classifier for meteorological timeseries data. The block entropy estimates define the entropy growth curve H(L) with respect to block length L. For a finitary process, the entropy growth curve tends to an asymptotic linear regime H(L) = E + hμL, with entropy rate hμ and excess entropy E. These quantities apportion the system's information content into ‘memory’ (E) and ‘randomness’ (hμ). We discuss the challenges inherent in analyzing weather data using symbolic techniques, identifying the pitfalls associated with alphabet size, finite sample timeseries length, and stationarity. We apply the block entropy-based techniques in the form of a wet/dry partition to Australian daily precipitation data from the Patched Point Dataset station record collection and version 3 of the Australian Water Availability Project analysis dataset. Preliminary results demonstrate hμ and E are viable climatological classifiers for precipitation, with station records from similar climatic regimes possessing similar values of hμ and E. The resultant clustering reflects expected characteristics of local climatic memory and randomness. The AWAP results show weaker clustering than their PPD counterparts, with different E- and hμ-values reflecting respectively the relative biases and truncation errors in the AWAP analysis system. The entropy rates of convergence analysis rules out finite order Markov processes for orders falling within the range of block sizes considered.